Rational Orbits in Prehomogeneous Vector Spaces
Published:Dec 31, 2025 11:05
•1 min read
•ArXiv
Analysis
This paper investigates the structure of rational orbit spaces within specific prehomogeneous vector spaces. The results are significant because they provide parametrizations for important algebraic structures like composition algebras, Freudenthal algebras, and involutions of the second kind. This has implications for understanding and classifying these objects over a field.
Key Takeaways
- •Provides a parametrization of composition algebras.
- •Offers a parametric description of reduced Freudenthal algebras of dimensions 6 and 9.
- •Gives a parametrization for involutions of the second kind on central division algebras.
Reference
“The paper parametrizes composition algebras, Freudenthal algebras, and involutions of the second kind.”